ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Transitive set
▼ Ordinal number
▼ Cardinal number
▼ Set cardinality
▼ Singleton set
▼ Set of singletons
Definition D5359
Singleton map
Formulation 0
Let $X$ and $Y$ each be a D11: Set such that
(i) \begin{equation} \{ \{ x \} : x \in X \} \subseteq Y \end{equation}
The singleton map from $X$ to $Y$ is the D18: Map \begin{equation} X \to Y, \quad x \mapsto \{ x \} \end{equation}
Children
▶ D4493: Canonical singleton map